Myths about teaching can hold you back
- Year 11•
- Higher
Checking and securing understanding of moving between function notation and the definition
I can fluently move between function notation and the function it represents, including when the function has been altered.
- Year 11•
- Higher
Checking and securing understanding of moving between function notation and the definition
I can fluently move between function notation and the function it represents, including when the function has been altered.
Lesson details
Key learning points
- Changing the function changes what it represents
- The change in notation can be seen in the algebraic form of the function it represents
- If a specific linear function is considered, the effects of this can be seen clearly
Keywords
Function - A function is a mathematical relationship that uniquely maps values of one set to the values of another set.
Common misconception
A common error is to not substitute into all variable terms where there is more than one in a function. For example, 'Write a simplified expression for f$$(x+3)$$ when f$$(x)=x^2-4x$$'
Use brackets when substituting. For example, for 'Write a simplified expression for f$$(x+3)$$ when f$$(x)=x^2-4x$$' you would write f$$(x+3)=(x+3)^2-4(x+3)$$
To help you plan your year 11 maths lesson on: Checking and securing understanding of moving between function notation and the definition, download all teaching resources for free and adapt to suit your pupils' needs...
To help you plan your year 11 maths lesson on: Checking and securing understanding of moving between function notation and the definition, download all teaching resources for free and adapt to suit your pupils' needs.
The starter quiz will activate and check your pupils' prior knowledge, with versions available both with and without answers in PDF format.
We use learning cycles to break down learning into key concepts or ideas linked to the learning outcome. Each learning cycle features explanations with checks for understanding and practice tasks with feedback. All of this is found in our slide decks, ready for you to download and edit. The practice tasks are also available as printable worksheets and some lessons have additional materials with extra material you might need for teaching the lesson.
The assessment exit quiz will test your pupils' understanding of the key learning points.
Our video is a tool for planning, showing how other teachers might teach the lesson, offering helpful tips, modelled explanations and inspiration for your own delivery in the classroom. Plus, you can set it as homework or revision for pupils and keep their learning on track by sharing an online pupil version of this lesson.
Explore more key stage 4 maths lessons from the Transformations of graphs unit, dive into the full secondary maths curriculum, or learn more about lesson planning.
Licence
Prior knowledge starter quiz
6 Questions
Q1.A uniquely maps values from the domain to values in the range.
Q2.If $$\text{f}(x)= 5x-4$$ what is the value of $$\text{f}(3)$$ ?
Q3.If $$\text{g}(x)= x^2- 3x$$ what is the value of $$\text{g}(4)$$ ?
Q4.Expand and simplify $$(x+3)^2$$.
Q5.Simplify $$3(4(2x+1)-5)$$.
Q6.If $$\text{f}(x) = 2x + 4$$ and $$\text{g}(x) = 3x- 2$$, what is an expression for $$\text{fg}(x)$$ ?
Assessment exit quiz
6 Questions
Q1.Match up these manipulations of $$\text{f}(x)$$ to their definitions.
$$\text{f}(x+3)$$ -Â
Add 3 to the given value of $$x$$ then substitute into the function.
$$\text{f}(x)+3$$ -Â
Evaluate the function for the given value of $$x$$ then add 3
$$\text{f}(3x)$$ -Â
Multiply $$x$$ by 3 then substitute this value into the function
$$3\text{f}(x)$$ -Â
Evaluate the function for the given value of $$x$$ then multiply by 3
Q2.If $$\text{g}(x)=3x-5$$ match up these manipulation to their value when $$x=3$$.
$$\text{g}(x+2)$$ -Â
$$10$$
$$\text{g}(x) + 2$$ -Â
$$6$$
$$\text{g}(2x)$$ -Â
$$13$$
$$2\text{g}(x)$$ -Â
$$8$$